LMFDB - Embedded newform 6019.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69112 q^{2} +1.73469 q^{3} +5.24211 q^{4} +2.53592 q^{5} -4.66825 q^{6} -4.16450 q^{7} -8.72491 q^{8} +0.00913932 q^{9} +O(q^{10})$	\(q-2.69112 q^{2} +1.73469 q^{3} +5.24211 q^{4} +2.53592 q^{5} -4.66825 q^{6} -4.16450 q^{7} -8.72491 q^{8} +0.00913932 q^{9} -6.82446 q^{10} +3.51668 q^{11} +9.09343 q^{12} -1.00000 q^{13} +11.2072 q^{14} +4.39903 q^{15} +12.9955 q^{16} -3.28147 q^{17} -0.0245950 q^{18} -1.88765 q^{19} +13.2936 q^{20} -7.22411 q^{21} -9.46381 q^{22} +2.67590 q^{23} -15.1350 q^{24} +1.43088 q^{25} +2.69112 q^{26} -5.18821 q^{27} -21.8308 q^{28} -6.30503 q^{29} -11.8383 q^{30} +9.03952 q^{31} -17.5227 q^{32} +6.10035 q^{33} +8.83083 q^{34} -10.5608 q^{35} +0.0479094 q^{36} +5.78425 q^{37} +5.07989 q^{38} -1.73469 q^{39} -22.1257 q^{40} +9.26736 q^{41} +19.4409 q^{42} +7.61549 q^{43} +18.4349 q^{44} +0.0231766 q^{45} -7.20117 q^{46} -2.85961 q^{47} +22.5432 q^{48} +10.3431 q^{49} -3.85068 q^{50} -5.69233 q^{51} -5.24211 q^{52} -8.73856 q^{53} +13.9621 q^{54} +8.91803 q^{55} +36.3349 q^{56} -3.27448 q^{57} +16.9676 q^{58} +10.0778 q^{59} +23.0602 q^{60} +10.1906 q^{61} -24.3264 q^{62} -0.0380607 q^{63} +21.1645 q^{64} -2.53592 q^{65} -16.4168 q^{66} -10.1721 q^{67} -17.2018 q^{68} +4.64185 q^{69} +28.4205 q^{70} +4.57723 q^{71} -0.0797398 q^{72} -6.10474 q^{73} -15.5661 q^{74} +2.48214 q^{75} -9.89528 q^{76} -14.6452 q^{77} +4.66825 q^{78} -3.75175 q^{79} +32.9556 q^{80} -9.02733 q^{81} -24.9396 q^{82} -14.8258 q^{83} -37.8696 q^{84} -8.32155 q^{85} -20.4942 q^{86} -10.9372 q^{87} -30.6828 q^{88} +8.10164 q^{89} -0.0623709 q^{90} +4.16450 q^{91} +14.0274 q^{92} +15.6807 q^{93} +7.69554 q^{94} -4.78693 q^{95} -30.3964 q^{96} -0.380863 q^{97} -27.8345 q^{98} +0.0321401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.69112	−1.90291	−0.951454	−	0.307792i	$-0.900410\pi$
$2$	−2.69112	−1.90291	−0.951454	+	0.307792i	$0.900410\pi$
$3$	1.73469	1.00152	0.500761	−	0.865586i	$-0.333054\pi$
$3$	1.73469	1.00152	0.500761	+	0.865586i	$0.333054\pi$
$4$	5.24211	2.62106
$5$	2.53592	1.13410	0.567049	−	0.823684i	$-0.308085\pi$
$5$	2.53592	1.13410	0.567049	+	0.823684i	$0.308085\pi$
$6$	−4.66825	−1.90580
$7$	−4.16450	−1.57403	−0.787017	−	0.616931i	$-0.788376\pi$
$7$	−4.16450	−1.57403	−0.787017	+	0.616931i	$0.788376\pi$
$8$	−8.72491	−3.08472
$9$	0.00913932	0.00304644
$10$	−6.82446	−2.15808
$11$	3.51668	1.06032	0.530160	−	0.847898i	$-0.322132\pi$
$11$	3.51668	1.06032	0.530160	+	0.847898i	$0.322132\pi$
$12$	9.09343	2.62505
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	11.2072	2.99524
$15$	4.39903	1.13582
$16$	12.9955	3.24888
$17$	−3.28147	−0.795874	−0.397937	−	0.917413i	$-0.630274\pi$
$17$	−3.28147	−0.795874	−0.397937	+	0.917413i	$0.630274\pi$
$18$	−0.0245950	−0.00579709
$19$	−1.88765	−0.433057	−0.216528	−	0.976276i	$-0.569473\pi$
$19$	−1.88765	−0.433057	−0.216528	+	0.976276i	$0.569473\pi$
$20$	13.2936	2.97253
$21$	−7.22411	−1.57643
$22$	−9.46381	−2.01769
$23$	2.67590	0.557964	0.278982	−	0.960296i	$-0.410003\pi$
$23$	2.67590	0.557964	0.278982	+	0.960296i	$0.410003\pi$
$24$	−15.1350	−3.08942
$25$	1.43088	0.286177
$26$	2.69112	0.527772
$27$	−5.18821	−0.998471
$28$	−21.8308	−4.12563
$29$	−6.30503	−1.17081	−0.585407	−	0.810740i	$-0.699065\pi$
$29$	−6.30503	−1.17081	−0.585407	+	0.810740i	$0.699065\pi$
$30$	−11.8383	−2.16137
$31$	9.03952	1.62355	0.811773	−	0.583973i	$-0.198503\pi$
$31$	9.03952	1.62355	0.811773	+	0.583973i	$0.198503\pi$
$32$	−17.5227	−3.09760
$33$	6.10035	1.06193
$34$	8.83083	1.51447
$35$	−10.5608	−1.78511
$36$	0.0479094	0.00798489
$37$	5.78425	0.950925	0.475462	−	0.879736i	$-0.342281\pi$
$37$	5.78425	0.950925	0.475462	+	0.879736i	$0.342281\pi$
$38$	5.07989	0.824067
$39$	−1.73469	−0.277772
$40$	−22.1257	−3.49837
$41$	9.26736	1.44732	0.723659	−	0.690157i	$-0.242459\pi$
$41$	9.26736	1.44732	0.723659	+	0.690157i	$0.242459\pi$
$42$	19.4409	2.99980
$43$	7.61549	1.16135	0.580676	−	0.814135i	$-0.302788\pi$
$43$	7.61549	1.16135	0.580676	+	0.814135i	$0.302788\pi$
$44$	18.4349	2.77916
$45$	0.0231766	0.00345496
$46$	−7.20117	−1.06175
$47$	−2.85961	−0.417117	−0.208558	−	0.978010i	$-0.566877\pi$
$47$	−2.85961	−0.417117	−0.208558	+	0.978010i	$0.566877\pi$
$48$	22.5432	3.25383
$49$	10.3431	1.47758
$50$	−3.85068	−0.544568
$51$	−5.69233	−0.797085
$52$	−5.24211	−0.726950
$53$	−8.73856	−1.20033	−0.600167	−	0.799875i	$-0.704899\pi$
$53$	−8.73856	−1.20033	−0.600167	+	0.799875i	$0.704899\pi$
$54$	13.9621	1.90000
$55$	8.91803	1.20251
$56$	36.3349	4.85546
$57$	−3.27448	−0.433716
$58$	16.9676	2.22795
$59$	10.0778	1.31201	0.656007	−	0.754755i	$-0.272244\pi$
$59$	10.0778	1.31201	0.656007	+	0.754755i	$0.272244\pi$
$60$	23.0602	2.97706
$61$	10.1906	1.30477	0.652384	−	0.757888i	$-0.273769\pi$
$61$	10.1906	1.30477	0.652384	+	0.757888i	$0.273769\pi$
$62$	−24.3264	−3.08946
$63$	−0.0380607	−0.00479520
$64$	21.1645	2.64557
$65$	−2.53592	−0.314542
$66$	−16.4168	−2.02076
$67$	−10.1721	−1.24271	−0.621357	−	0.783528i	$-0.713418\pi$
$67$	−10.1721	−1.24271	−0.621357	+	0.783528i	$0.713418\pi$
$68$	−17.2018	−2.08603
$69$	4.64185	0.558814
$70$	28.4205	3.39690
$71$	4.57723	0.543217	0.271609	−	0.962408i	$-0.412444\pi$
$71$	4.57723	0.543217	0.271609	+	0.962408i	$0.412444\pi$
$72$	−0.0797398	−0.00939742
$73$	−6.10474	−0.714506	−0.357253	−	0.934008i	$-0.616287\pi$
$73$	−6.10474	−0.714506	−0.357253	+	0.934008i	$0.616287\pi$
$74$	−15.5661	−1.80952
$75$	2.48214	0.286612
$76$	−9.89528	−1.13507
$77$	−14.6452	−1.66898
$78$	4.66825	0.528575
$79$	−3.75175	−0.422105	−0.211053	−	0.977475i	$-0.567689\pi$
$79$	−3.75175	−0.422105	−0.211053	+	0.977475i	$0.567689\pi$
$80$	32.9556	3.68455
$81$	−9.02733	−1.00304
$82$	−24.9396	−2.75411
$83$	−14.8258	−1.62735	−0.813673	−	0.581322i	$-0.802536\pi$
$83$	−14.8258	−1.62735	−0.813673	+	0.581322i	$0.802536\pi$
$84$	−37.8696	−4.13191
$85$	−8.32155	−0.902598
$86$	−20.4942	−2.20995
$87$	−10.9372	−1.17260
$88$	−30.6828	−3.27079
$89$	8.10164	0.858772	0.429386	−	0.903121i	$-0.358730\pi$
$89$	8.10164	0.858772	0.429386	+	0.903121i	$0.358730\pi$
$90$	−0.0623709	−0.00657447
$91$	4.16450	0.436559
$92$	14.0274	1.46246
$93$	15.6807	1.62602
$94$	7.69554	0.793734
$95$	−4.78693	−0.491128
$96$	−30.3964	−3.10232
$97$	−0.380863	−0.0386708	−0.0193354	−	0.999813i	$-0.506155\pi$
$97$	−0.380863	−0.0386708	−0.0193354	+	0.999813i	$0.506155\pi$
$98$	−27.8345	−2.81171
$99$	0.0321401	0.00323020
$100$	7.50086	0.750086
$101$	−8.50290	−0.846070	−0.423035	−	0.906113i	$-0.639035\pi$
$101$	−8.50290	−0.846070	−0.423035	+	0.906113i	$0.639035\pi$
$102$	15.3187	1.51678
$103$	12.8556	1.26670	0.633352	−	0.773864i	$-0.281679\pi$
$103$	12.8556	1.26670	0.633352	+	0.773864i	$0.281679\pi$
$104$	8.72491	0.855548
$105$	−18.3198	−1.78783
$106$	23.5165	2.28412
$107$	6.45658	0.624181	0.312091	−	0.950052i	$-0.398971\pi$
$107$	6.45658	0.624181	0.312091	+	0.950052i	$0.398971\pi$
$108$	−27.1972	−2.61705
$109$	9.60963	0.920436	0.460218	−	0.887806i	$-0.347771\pi$
$109$	9.60963	0.920436	0.460218	+	0.887806i	$0.347771\pi$
$110$	−23.9995	−2.28826
$111$	10.0339	0.952372
$112$	−54.1199	−5.11385
$113$	15.4234	1.45091	0.725455	−	0.688269i	$-0.241629\pi$
$113$	15.4234	1.45091	0.725455	+	0.688269i	$0.241629\pi$
$114$	8.81202	0.825321
$115$	6.78587	0.632786
$116$	−33.0517	−3.06877
$117$	−0.00913932	−0.000844931 0
$118$	−27.1205	−2.49664
$119$	13.6657	1.25273
$120$	−38.3811	−3.50370
$121$	1.36707	0.124279
$122$	−27.4240	−2.48285
$123$	16.0760	1.44952
$124$	47.3862	4.25541
$125$	−9.05099	−0.809545
$126$	0.102426	0.00912483
$127$	−4.74069	−0.420668	−0.210334	−	0.977630i	$-0.567455\pi$
$127$	−4.74069	−0.420668	−0.210334	+	0.977630i	$0.567455\pi$
$128$	−21.9109	−1.93667
$129$	13.2105	1.16312
$130$	6.82446	0.598544
$131$	−0.399096	−0.0348692	−0.0174346	−	0.999848i	$-0.505550\pi$
$131$	−0.399096	−0.0348692	−0.0174346	+	0.999848i	$0.505550\pi$
$132$	31.9787	2.78339
$133$	7.86113	0.681646
$134$	27.3742	2.36477
$135$	−13.1569	−1.13236
$136$	28.6305	2.45505
$137$	19.6596	1.67963	0.839816	−	0.542870i	$-0.182663\pi$
$137$	19.6596	1.67963	0.839816	+	0.542870i	$0.182663\pi$
$138$	−12.4918	−1.06337
$139$	−16.4665	−1.39667	−0.698335	−	0.715771i	$-0.746076\pi$
$139$	−16.4665	−1.39667	−0.698335	+	0.715771i	$0.746076\pi$
$140$	−55.3612	−4.67887
$141$	−4.96052	−0.417751
$142$	−12.3179	−1.03369
$143$	−3.51668	−0.294080
$144$	0.118770	0.00989753
$145$	−15.9890	−1.32782
$146$	16.4286	1.35964
$147$	17.9420	1.47983
$148$	30.3217	2.49243
$149$	11.5571	0.946797	0.473399	−	0.880848i	$-0.343027\pi$
$149$	11.5571	0.946797	0.473399	+	0.880848i	$0.343027\pi$
$150$	−6.67972	−0.545397
$151$	7.05886	0.574442	0.287221	−	0.957864i	$-0.407269\pi$
$151$	7.05886	0.574442	0.287221	+	0.957864i	$0.407269\pi$
$152$	16.4696	1.33586
$153$	−0.0299904	−0.00242458
$154$	39.4121	3.17592
$155$	22.9235	1.84126
$156$	−9.09343	−0.728057
$157$	−9.46490	−0.755381	−0.377691	−	0.925932i	$-0.623282\pi$
$157$	−9.46490	−0.755381	−0.377691	+	0.925932i	$0.623282\pi$
$158$	10.0964	0.803227
$159$	−15.1587	−1.20216
$160$	−44.4361	−3.51298
$161$	−11.1438	−0.878255
$162$	24.2936	1.90869
$163$	10.1607	0.795846	0.397923	−	0.917419i	$-0.369731\pi$
$163$	10.1607	0.795846	0.397923	+	0.917419i	$0.369731\pi$
$164$	48.5806	3.79350
$165$	15.4700	1.20434
$166$	39.8981	3.09669
$167$	14.7237	1.13935	0.569677	−	0.821869i	$-0.307068\pi$
$167$	14.7237	1.13935	0.569677	+	0.821869i	$0.307068\pi$
$168$	63.0297	4.86285
$169$	1.00000	0.0769231
$170$	22.3943	1.71756
$171$	−0.0172518	−0.00131928
$172$	39.9213	3.04397
$173$	−9.62376	−0.731681	−0.365840	−	0.930678i	$-0.619218\pi$
$173$	−9.62376	−0.731681	−0.365840	+	0.930678i	$0.619218\pi$
$174$	29.4334	2.23134
$175$	−5.95892	−0.450452
$176$	45.7012	3.44486
$177$	17.4818	1.31401
$178$	−21.8025	−1.63416
$179$	−5.87637	−0.439221	−0.219610	−	0.975588i	$-0.570479\pi$
$179$	−5.87637	−0.439221	−0.219610	+	0.975588i	$0.570479\pi$
$180$	0.121494	0.00905565
$181$	13.3596	0.993015	0.496507	−	0.868033i	$-0.334616\pi$
$181$	13.3596	0.993015	0.496507	+	0.868033i	$0.334616\pi$
$182$	−11.2072	−0.830731
$183$	17.6774	1.30675
$184$	−23.3470	−1.72116
$185$	14.6684	1.07844
$186$	−42.1987	−3.09416
$187$	−11.5399	−0.843881
$188$	−14.9904	−1.09329
$189$	21.6063	1.57163
$190$	12.8822	0.934572
$191$	11.4436	0.828031	0.414016	−	0.910270i	$-0.364126\pi$
$191$	11.4436	0.828031	0.414016	+	0.910270i	$0.364126\pi$
$192$	36.7139	2.64959
$193$	19.0662	1.37241	0.686207	−	0.727406i	$-0.259274\pi$
$193$	19.0662	1.37241	0.686207	+	0.727406i	$0.259274\pi$
$194$	1.02495	0.0735869
$195$	−4.39903	−0.315021
$196$	54.2197	3.87283
$197$	17.3067	1.23305	0.616526	−	0.787335i	$-0.288540\pi$
$197$	17.3067	1.23305	0.616526	+	0.787335i	$0.288540\pi$
$198$	−0.0864928	−0.00614678
$199$	−7.36672	−0.522213	−0.261107	−	0.965310i	$-0.584087\pi$
$199$	−7.36672	−0.522213	−0.261107	+	0.965310i	$0.584087\pi$
$200$	−12.4843	−0.882776
$201$	−17.6453	−1.24461
$202$	22.8823	1.60999
$203$	26.2573	1.84290
$204$	−29.8398	−2.08921
$205$	23.5013	1.64140
$206$	−34.5960	−2.41042
$207$	0.0244559	0.00169981
$208$	−12.9955	−0.901078
$209$	−6.63827	−0.459179
$210$	49.3006	3.40207
$211$	13.5350	0.931791	0.465895	−	0.884840i	$-0.345732\pi$
$211$	13.5350	0.931791	0.465895	+	0.884840i	$0.345732\pi$
$212$	−45.8085	−3.14614
$213$	7.94006	0.544044
$214$	−17.3754	−1.18776
$215$	19.3123	1.31709
$216$	45.2666	3.08001
$217$	−37.6451	−2.55552
$218$	−25.8606	−1.75150
$219$	−10.5898	−0.715593
$220$	46.7493	3.15184
$221$	3.28147	0.220736
$222$	−27.0023	−1.81228
$223$	−24.6648	−1.65168	−0.825840	−	0.563905i	$-0.809298\pi$
$223$	−24.6648	−1.65168	−0.825840	+	0.563905i	$0.809298\pi$
$224$	72.9733	4.87573
$225$	0.0130773	0.000871821 0
$226$	−41.5062	−2.76095
$227$	3.25598	0.216107	0.108053	−	0.994145i	$-0.465538\pi$
$227$	3.25598	0.216107	0.108053	+	0.994145i	$0.465538\pi$
$228$	−17.1652	−1.13679
$229$	−15.1038	−0.998087	−0.499044	−	0.866577i	$-0.666315\pi$
$229$	−15.1038	−0.998087	−0.499044	+	0.866577i	$0.666315\pi$
$230$	−18.2616	−1.20413
$231$	−25.4049	−1.67152
$232$	55.0108	3.61164
$233$	13.2716	0.869454	0.434727	−	0.900562i	$-0.356845\pi$
$233$	13.2716	0.869454	0.434727	+	0.900562i	$0.356845\pi$
$234$	0.0245950	0.00160782
$235$	−7.25173	−0.473051
$236$	52.8288	3.43886
$237$	−6.50812	−0.422748
$238$	−36.7760	−2.38383
$239$	6.39194	0.413460	0.206730	−	0.978398i	$-0.433718\pi$
$239$	6.39194	0.413460	0.206730	+	0.978398i	$0.433718\pi$
$240$	57.1677	3.69016
$241$	−14.4323	−0.929669	−0.464835	−	0.885397i	$-0.653886\pi$
$241$	−14.4323	−0.929669	−0.464835	+	0.885397i	$0.653886\pi$
$242$	−3.67895	−0.236492
$243$	−0.0949783	−0.00609286
$244$	53.4201	3.41987
$245$	26.2292	1.67572
$246$	−43.2623	−2.75831
$247$	1.88765	0.120108
$248$	−78.8690	−5.00819
$249$	−25.7182	−1.62982
$250$	24.3573	1.54049
$251$	27.4303	1.73139	0.865693	−	0.500576i	$-0.166878\pi$
$251$	27.4303	1.73139	0.865693	+	0.500576i	$0.166878\pi$
$252$	−0.199519	−0.0125685
$253$	9.41031	0.591621
$254$	12.7577	0.800492
$255$	−14.4353	−0.903972
$256$	16.6357	1.03973
$257$	−13.3298	−0.831493	−0.415746	−	0.909481i	$-0.636480\pi$
$257$	−13.3298	−0.831493	−0.415746	+	0.909481i	$0.636480\pi$
$258$	−35.5510	−2.21331
$259$	−24.0885	−1.49679
$260$	−13.2936	−0.824433
$261$	−0.0576237	−0.00356681
$262$	1.07402	0.0663529
$263$	18.8577	1.16282	0.581409	−	0.813611i	$-0.302502\pi$
$263$	18.8577	1.16282	0.581409	+	0.813611i	$0.302502\pi$
$264$	−53.2250	−3.27577
$265$	−22.1603	−1.36130
$266$	−21.1552	−1.29711
$267$	14.0538	0.860079
$268$	−53.3231	−3.25722
$269$	−8.86783	−0.540681	−0.270341	−	0.962765i	$-0.587136\pi$
$269$	−8.86783	−0.540681	−0.270341	+	0.962765i	$0.587136\pi$
$270$	35.4067	2.15478
$271$	30.0217	1.82369	0.911843	−	0.410539i	$-0.134660\pi$
$271$	30.0217	1.82369	0.911843	+	0.410539i	$0.134660\pi$
$272$	−42.6445	−2.58570
$273$	7.22411	0.437223
$274$	−52.9063	−3.19619
$275$	5.03197	0.303439
$276$	24.3331	1.46468
$277$	23.3207	1.40121	0.700604	−	0.713551i	$-0.252914\pi$
$277$	23.3207	1.40121	0.700604	+	0.713551i	$0.252914\pi$
$278$	44.3133	2.65774
$279$	0.0826151	0.00494604
$280$	92.1424	5.50656
$281$	27.4529	1.63770	0.818850	−	0.574008i	$-0.194612\pi$
$281$	27.4529	1.63770	0.818850	+	0.574008i	$0.194612\pi$
$282$	13.3494	0.794942
$283$	1.74124	0.103506	0.0517530	−	0.998660i	$-0.483519\pi$
$283$	1.74124	0.103506	0.0517530	+	0.998660i	$0.483519\pi$
$284$	23.9944	1.42380
$285$	−8.30382	−0.491876
$286$	9.46381	0.559607
$287$	−38.5940	−2.27813
$288$	−0.160145	−0.00943666
$289$	−6.23194	−0.366585
$290$	43.0284	2.52671
$291$	−0.660678	−0.0387296
$292$	−32.0017	−1.87276
$293$	20.7703	1.21341	0.606707	−	0.794926i	$-0.292490\pi$
$293$	20.7703	1.21341	0.606707	+	0.794926i	$0.292490\pi$
$294$	−48.2841	−2.81599
$295$	25.5564	1.48795
$296$	−50.4670	−2.93334
$297$	−18.2453	−1.05870
$298$	−31.1016	−1.80167
$299$	−2.67590	−0.154751
$300$	13.0116	0.751228
$301$	−31.7148	−1.82801
$302$	−18.9962	−1.09311
$303$	−14.7499	−0.847358
$304$	−24.5310	−1.40695
$305$	25.8425	1.47973
$306$	0.0807078	0.00461376
$307$	15.2080	0.867968	0.433984	−	0.900921i	$-0.357107\pi$
$307$	15.2080	0.867968	0.433984	+	0.900921i	$0.357107\pi$
$308$	−76.7721	−4.37449
$309$	22.3005	1.26863
$310$	−61.6898	−3.50375
$311$	−23.4600	−1.33029	−0.665147	−	0.746712i	$-0.731631\pi$
$311$	−23.4600	−1.33029	−0.665147	+	0.746712i	$0.731631\pi$
$312$	15.1350	0.856850
$313$	−5.70944	−0.322716	−0.161358	−	0.986896i	$-0.551587\pi$
$313$	−5.70944	−0.322716	−0.161358	+	0.986896i	$0.551587\pi$
$314$	25.4712	1.43742
$315$	−0.0965190	−0.00543823
$316$	−19.6671	−1.10636
$317$	5.73861	0.322312	0.161156	−	0.986929i	$-0.448478\pi$
$317$	5.73861	0.322312	0.161156	+	0.986929i	$0.448478\pi$
$318$	40.7938	2.28760
$319$	−22.1728	−1.24144
$320$	53.6716	3.00033
$321$	11.2001	0.625131
$322$	29.9893	1.67124
$323$	6.19427	0.344658
$324$	−47.3223	−2.62902
$325$	−1.43088	−0.0793712
$326$	−27.3436	−1.51442
$327$	16.6697	0.921837
$328$	−80.8569	−4.46457
$329$	11.9088	0.656556
$330$	−41.6316	−2.29174
$331$	29.3728	1.61448	0.807239	−	0.590225i	$-0.200961\pi$
$331$	29.3728	1.61448	0.807239	+	0.590225i	$0.200961\pi$
$332$	−77.7187	−4.26537
$333$	0.0528641	0.00289694
$334$	−39.6232	−2.16808
$335$	−25.7955	−1.40936
$336$	−93.8812	−5.12164
$337$	−9.53442	−0.519373	−0.259686	−	0.965693i	$-0.583619\pi$
$337$	−9.53442	−0.519373	−0.259686	+	0.965693i	$0.583619\pi$
$338$	−2.69112	−0.146378
$339$	26.7548	1.45312
$340$	−43.6225	−2.36576
$341$	31.7892	1.72148
$342$	0.0464267	0.00251047
$343$	−13.9223	−0.751735
$344$	−66.4445	−3.58245
$345$	11.7714	0.633749
$346$	25.8987	1.39232
$347$	9.83712	0.528084	0.264042	−	0.964511i	$-0.414944\pi$
$347$	9.83712	0.528084	0.264042	+	0.964511i	$0.414944\pi$
$348$	−57.3343	−3.07344
$349$	−24.3626	−1.30410	−0.652051	−	0.758175i	$-0.726091\pi$
$349$	−24.3626	−1.30410	−0.652051	+	0.758175i	$0.726091\pi$
$350$	16.0362	0.857169
$351$	5.18821	0.276926
$352$	−61.6218	−3.28445
$353$	36.1480	1.92396	0.961981	−	0.273117i	$-0.0880548\pi$
$353$	36.1480	1.92396	0.961981	+	0.273117i	$0.0880548\pi$
$354$	−47.0455	−2.50044
$355$	11.6075	0.616061
$356$	42.4697	2.25089
$357$	23.7057	1.25464
$358$	15.8140	0.835796
$359$	13.0831	0.690501	0.345250	−	0.938511i	$-0.387794\pi$
$359$	13.0831	0.690501	0.345250	+	0.938511i	$0.387794\pi$
$360$	−0.202214	−0.0106576
$361$	−15.4368	−0.812462
$362$	−35.9524	−1.88962
$363$	2.37144	0.124468
$364$	21.8308	1.14425
$365$	−15.4811	−0.810319
$366$	−47.5721	−2.48663
$367$	12.6715	0.661448	0.330724	−	0.943728i	$-0.392707\pi$
$367$	12.6715	0.661448	0.330724	+	0.943728i	$0.392707\pi$
$368$	34.7748	1.81276
$369$	0.0846974	0.00440917
$370$	−39.4743	−2.05217
$371$	36.3918	1.88937
$372$	82.2003	4.26188
$373$	−7.87145	−0.407568	−0.203784	−	0.979016i	$-0.565324\pi$
$373$	−7.87145	−0.407568	−0.203784	+	0.979016i	$0.565324\pi$
$374$	31.0552	1.60583
$375$	−15.7006	−0.810777
$376$	24.9498	1.28669
$377$	6.30503	0.324725
$378$	−58.1451	−2.99066
$379$	0.327091	0.0168015	0.00840076	−	0.999965i	$-0.497326\pi$
$379$	0.327091	0.0168015	0.00840076	+	0.999965i	$0.497326\pi$
$380$	−25.0936	−1.28728
$381$	−8.22361	−0.421308
$382$	−30.7961	−1.57567
$383$	2.10600	0.107612	0.0538059	−	0.998551i	$-0.482865\pi$
$383$	2.10600	0.107612	0.0538059	+	0.998551i	$0.482865\pi$
$384$	−38.0086	−1.93962
$385$	−37.1392	−1.89279
$386$	−51.3094	−2.61158
$387$	0.0696005	0.00353799
$388$	−1.99653	−0.101358
$389$	19.7077	0.999221	0.499611	−	0.866250i	$-0.333476\pi$
$389$	19.7077	0.999221	0.499611	+	0.866250i	$0.333476\pi$
$390$	11.8383	0.599455
$391$	−8.78090	−0.444069
$392$	−90.2426	−4.55794
$393$	−0.692307	−0.0349223
$394$	−46.5744	−2.34638
$395$	−9.51414	−0.478709
$396$	0.168482	0.00846655
$397$	−9.05023	−0.454218	−0.227109	−	0.973869i	$-0.572927\pi$
$397$	−9.05023	−0.454218	−0.227109	+	0.973869i	$0.572927\pi$
$398$	19.8247	0.993723
$399$	13.6366	0.682684
$400$	18.5951	0.929755
$401$	−26.3535	−1.31603	−0.658015	−	0.753005i	$-0.728604\pi$
$401$	−26.3535	−1.31603	−0.658015	+	0.753005i	$0.728604\pi$
$402$	47.4857	2.36837
$403$	−9.03952	−0.450291
$404$	−44.5732	−2.21760
$405$	−22.8926	−1.13754
$406$	−70.6615	−3.50687
$407$	20.3414	1.00828
$408$	49.6650	2.45879
$409$	−19.8551	−0.981772	−0.490886	−	0.871224i	$-0.663327\pi$
$409$	−19.8551	−0.981772	−0.490886	+	0.871224i	$0.663327\pi$
$410$	−63.2447	−3.12343
$411$	34.1033	1.68219
$412$	67.3907	3.32010
$413$	−41.9689	−2.06515
$414$	−0.0658138	−0.00323457
$415$	−37.5971	−1.84557
$416$	17.5227	0.859120
$417$	−28.5642	−1.39880
$418$	17.8644	0.873775
$419$	2.03770	0.0995481	0.0497741	−	0.998761i	$-0.484150\pi$
$419$	2.03770	0.0995481	0.0497741	+	0.998761i	$0.484150\pi$
$420$	−96.0343	−4.68599
$421$	38.4689	1.87486	0.937429	−	0.348178i	$-0.113199\pi$
$421$	38.4689	1.87486	0.937429	+	0.348178i	$0.113199\pi$
$422$	−36.4244	−1.77311
$423$	−0.0261349	−0.00127072
$424$	76.2432	3.70270
$425$	−4.69541	−0.227761
$426$	−21.3676	−1.03527
$427$	−42.4387	−2.05375
$428$	33.8461	1.63601
$429$	−6.10035	−0.294528
$430$	−51.9716	−2.50629
$431$	−36.2972	−1.74838	−0.874188	−	0.485587i	$-0.838606\pi$
$431$	−36.2972	−1.74838	−0.874188	+	0.485587i	$0.838606\pi$
$432$	−67.4235	−3.24392
$433$	−34.4635	−1.65621	−0.828104	−	0.560574i	$-0.810580\pi$
$433$	−34.4635	−1.65621	−0.828104	+	0.560574i	$0.810580\pi$
$434$	101.307	4.86291
$435$	−27.7360	−1.32984
$436$	50.3748	2.41251
$437$	−5.05117	−0.241630
$438$	28.4984	1.36171
$439$	36.9754	1.76474	0.882370	−	0.470556i	$-0.155947\pi$
$439$	36.9754	1.76474	0.882370	+	0.470556i	$0.155947\pi$
$440$	−77.8090	−3.70940
$441$	0.0945289	0.00450137
$442$	−8.83083	−0.420040
$443$	7.50478	0.356563	0.178281	−	0.983980i	$-0.442946\pi$
$443$	7.50478	0.356563	0.178281	+	0.983980i	$0.442946\pi$
$444$	52.5986	2.49622
$445$	20.5451	0.973931
$446$	66.3760	3.14299
$447$	20.0480	0.948238
$448$	−88.1398	−4.16422
$449$	9.53806	0.450129	0.225064	−	0.974344i	$-0.427741\pi$
$449$	9.53806	0.450129	0.225064	+	0.974344i	$0.427741\pi$
$450$	−0.0351926	−0.00165899
$451$	32.5904	1.53462
$452$	80.8512	3.80292
$453$	12.2449	0.575316
$454$	−8.76223	−0.411232
$455$	10.5608	0.495100
$456$	28.5696	1.33789
$457$	−5.15855	−0.241307	−0.120653	−	0.992695i	$-0.538499\pi$
$457$	−5.15855	−0.241307	−0.120653	+	0.992695i	$0.538499\pi$
$458$	40.6461	1.89927
$459$	17.0250	0.794657
$460$	35.5723	1.65857
$461$	13.6612	0.636267	0.318133	−	0.948046i	$-0.396944\pi$
$461$	13.6612	0.636267	0.318133	+	0.948046i	$0.396944\pi$
$462$	68.3676	3.18075
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−81.9372	−3.80384
$465$	39.7651	1.84406
$466$	−35.7156	−1.65449
$467$	26.1081	1.20814	0.604069	−	0.796932i	$-0.293545\pi$
$467$	26.1081	1.20814	0.604069	+	0.796932i	$0.293545\pi$
$468$	−0.0479094	−0.00221461
$469$	42.3616	1.95607
$470$	19.5153	0.900172
$471$	−16.4186	−0.756531
$472$	−87.9276	−4.04720
$473$	26.7813	1.23141
$474$	17.5141	0.804450
$475$	−2.70101	−0.123931
$476$	71.6372	3.28348
$477$	−0.0798645	−0.00365675
$478$	−17.2015	−0.786776
$479$	−17.3130	−0.791052	−0.395526	−	0.918455i	$-0.629438\pi$
$479$	−17.3130	−0.791052	−0.395526	+	0.918455i	$0.629438\pi$
$480$	−77.0827	−3.51833
$481$	−5.78425	−0.263739
$482$	38.8392	1.76907
$483$	−19.3310	−0.879592
$484$	7.16634	0.325743
$485$	−0.965838	−0.0438564
$486$	0.255598	0.0115941
$487$	19.2714	0.873270	0.436635	−	0.899639i	$-0.356170\pi$
$487$	19.2714	0.873270	0.436635	+	0.899639i	$0.356170\pi$
$488$	−88.9118	−4.02485
$489$	17.6256	0.797058
$490$	−70.5860	−3.18875
$491$	−21.2807	−0.960383	−0.480192	−	0.877164i	$-0.659433\pi$
$491$	−21.2807	−0.960383	−0.480192	+	0.877164i	$0.659433\pi$
$492$	84.2721	3.79928
$493$	20.6898	0.931820
$494$	−5.07989	−0.228555
$495$	0.0815047	0.00366336
$496$	117.473	5.27471
$497$	−19.0619	−0.855043
$498$	69.2107	3.10140
$499$	−39.4489	−1.76597	−0.882987	−	0.469397i	$-0.844471\pi$
$499$	−39.4489	−1.76597	−0.882987	+	0.469397i	$0.844471\pi$
$500$	−47.4463	−2.12186
$501$	25.5410	1.14109
$502$	−73.8182	−3.29467
$503$	−8.34070	−0.371893	−0.185947	−	0.982560i	$-0.559535\pi$
$503$	−8.34070	−0.371893	−0.185947	+	0.982560i	$0.559535\pi$
$504$	0.332077	0.0147919
$505$	−21.5627	−0.959526
$506$	−25.3242	−1.12580
$507$	1.73469	0.0770402
$508$	−24.8512	−1.10259
$509$	−34.3836	−1.52403	−0.762013	−	0.647562i	$-0.775789\pi$
$509$	−34.3836	−1.52403	−0.762013	+	0.647562i	$0.775789\pi$
$510$	38.8470	1.72018
$511$	25.4232	1.12466
$512$	−0.946923	−0.0418485
$513$	9.79352	0.432394
$514$	35.8722	1.58225
$515$	32.6009	1.43657
$516$	69.2510	3.04860
$517$	−10.0563	−0.442277
$518$	64.8251	2.84825
$519$	−16.6942	−0.732795
$520$	22.1257	0.970275
$521$	−20.8986	−0.915582	−0.457791	−	0.889060i	$-0.651359\pi$
$521$	−20.8986	−0.915582	−0.457791	+	0.889060i	$0.651359\pi$
$522$	0.155072	0.00678732
$523$	0.316406	0.0138355	0.00691773	−	0.999976i	$-0.497798\pi$
$523$	0.316406	0.0138355	0.00691773	+	0.999976i	$0.497798\pi$
$524$	−2.09211	−0.0913942
$525$	−10.3369	−0.451138
$526$	−50.7484	−2.21274
$527$	−29.6629	−1.29214
$528$	79.2773	3.45010
$529$	−15.8395	−0.688676
$530$	59.6359	2.59042
$531$	0.0921039	0.00399697
$532$	41.2089	1.78663
$533$	−9.26736	−0.401414
$534$	−37.8204	−1.63665
$535$	16.3734	0.707882
$536$	88.7503	3.83343
$537$	−10.1937	−0.439889
$538$	23.8644	1.02887
$539$	36.3734	1.56671
$540$	−68.9698	−2.96799
$541$	−9.50933	−0.408838	−0.204419	−	0.978883i	$-0.565531\pi$
$541$	−9.50933	−0.408838	−0.204419	+	0.978883i	$0.565531\pi$
$542$	−80.7918	−3.47031
$543$	23.1748	0.994526
$544$	57.5002	2.46530
$545$	24.3692	1.04386
$546$	−19.4409	−0.831995
$547$	−11.4540	−0.489739	−0.244869	−	0.969556i	$-0.578745\pi$
$547$	−11.4540	−0.489739	−0.244869	+	0.969556i	$0.578745\pi$
$548$	103.058	4.40241
$549$	0.0931349	0.00397490
$550$	−13.5416	−0.577417
$551$	11.9017	0.507029
$552$	−40.4998	−1.72378
$553$	15.6242	0.664408
$554$	−62.7589	−2.66637
$555$	25.4451	1.08008
$556$	−86.3193	−3.66075
$557$	31.7979	1.34732	0.673660	−	0.739042i	$-0.264721\pi$
$557$	31.7979	1.34732	0.673660	+	0.739042i	$0.264721\pi$
$558$	−0.222327	−0.00941185
$559$	−7.61549	−0.322101
$560$	−137.244	−5.79961
$561$	−20.0181	−0.845166
$562$	−73.8789	−3.11639
$563$	−23.4622	−0.988812	−0.494406	−	0.869231i	$-0.664614\pi$
$563$	−23.4622	−0.988812	−0.494406	+	0.869231i	$0.664614\pi$
$564$	−26.0036	−1.09495
$565$	39.1125	1.64547
$566$	−4.68588	−0.196962
$567$	37.5944	1.57882
$568$	−39.9359	−1.67567
$569$	25.4516	1.06699	0.533493	−	0.845804i	$-0.320879\pi$
$569$	25.4516	1.06699	0.533493	+	0.845804i	$0.320879\pi$
$570$	22.3466	0.935994
$571$	−35.8591	−1.50066	−0.750328	−	0.661066i	$-0.770104\pi$
$571$	−35.8591	−1.50066	−0.750328	+	0.661066i	$0.770104\pi$
$572$	−18.4349	−0.770800
$573$	19.8511	0.829291
$574$	103.861	4.33507
$575$	3.82891	0.159677
$576$	0.193430	0.00805957
$577$	−24.2808	−1.01082	−0.505411	−	0.862879i	$-0.668659\pi$
$577$	−24.2808	−1.01082	−0.505411	+	0.862879i	$0.668659\pi$
$578$	16.7709	0.697577
$579$	33.0739	1.37450
$580$	−83.8163	−3.48028
$581$	61.7422	2.56150
$582$	1.77796	0.0736989
$583$	−30.7308	−1.27274
$584$	53.2633	2.20405
$585$	−0.0231766	−0.000958234 0
$586$	−55.8953	−2.30901
$587$	−15.6942	−0.647769	−0.323885	−	0.946097i	$-0.604989\pi$
$587$	−15.6942	−0.647769	−0.323885	+	0.946097i	$0.604989\pi$
$588$	94.0542	3.87873
$589$	−17.0635	−0.703087
$590$	−68.7753	−2.83143
$591$	30.0217	1.23493
$592$	75.1694	3.08944
$593$	−0.0228541	−0.000938505 0	−0.000469253	−	1.00000i	$-0.500149\pi$
$593$	−0.0228541	−0.000938505 0	−0.000469253		1.00000i	$0.500149\pi$
$594$	49.1002	2.01461
$595$	34.6551	1.42072
$596$	60.5838	2.48161
$597$	−12.7790	−0.523008
$598$	7.20117	0.294478
$599$	45.0996	1.84272	0.921360	−	0.388711i	$-0.127080\pi$
$599$	45.0996	1.84272	0.921360	+	0.388711i	$0.127080\pi$
$600$	−21.6564	−0.884120
$601$	22.3406	0.911292	0.455646	−	0.890161i	$-0.349408\pi$
$601$	22.3406	0.911292	0.455646	+	0.890161i	$0.349408\pi$
$602$	85.3481	3.47853
$603$	−0.0929657	−0.00378585
$604$	37.0033	1.50564
$605$	3.46678	0.140945
$606$	39.6937	1.61244
$607$	23.0983	0.937531	0.468766	−	0.883323i	$-0.344699\pi$
$607$	23.0983	0.937531	0.468766	+	0.883323i	$0.344699\pi$
$608$	33.0767	1.34144
$609$	45.5482	1.84571
$610$	−69.5451	−2.81580
$611$	2.85961	0.115687
$612$	−0.157213	−0.00635497
$613$	−22.9810	−0.928195	−0.464098	−	0.885784i	$-0.653621\pi$
$613$	−22.9810	−0.928195	−0.464098	+	0.885784i	$0.653621\pi$
$614$	−40.9266	−1.65166
$615$	40.7674	1.64390
$616$	127.778	5.14834
$617$	14.3435	0.577446	0.288723	−	0.957413i	$-0.406769\pi$
$617$	14.3435	0.577446	0.288723	+	0.957413i	$0.406769\pi$
$618$	−60.0133	−2.41409
$619$	−23.2802	−0.935710	−0.467855	−	0.883805i	$-0.654973\pi$
$619$	−23.2802	−0.935710	−0.467855	+	0.883805i	$0.654973\pi$
$620$	120.168	4.82605
$621$	−13.8831	−0.557111
$622$	63.1336	2.53143
$623$	−33.7393	−1.35174
$624$	−22.5432	−0.902450
$625$	−30.1070	−1.20428
$626$	15.3648	0.614099
$627$	−11.5153	−0.459878
$628$	−49.6161	−1.97990
$629$	−18.9808	−0.756816
$630$	0.259744	0.0103484
$631$	−7.58930	−0.302125	−0.151063	−	0.988524i	$-0.548269\pi$
$631$	−7.58930	−0.302125	−0.151063	+	0.988524i	$0.548269\pi$
$632$	32.7337	1.30208
$633$	23.4791	0.933209
$634$	−15.4433	−0.613331
$635$	−12.0220	−0.477078
$636$	−79.4635	−3.15093
$637$	−10.3431	−0.409808
$638$	59.6696	2.36234
$639$	0.0418328	0.00165488
$640$	−55.5643	−2.19637
$641$	−12.5983	−0.497601	−0.248800	−	0.968555i	$-0.580036\pi$
$641$	−12.5983	−0.497601	−0.248800	+	0.968555i	$0.580036\pi$
$642$	−30.1409	−1.18957
$643$	37.1438	1.46481	0.732404	−	0.680870i	$-0.238398\pi$
$643$	37.1438	1.46481	0.732404	+	0.680870i	$0.238398\pi$
$644$	−58.4171	−2.30196
$645$	33.5008	1.31909
$646$	−16.6695	−0.655853
$647$	4.03409	0.158596	0.0792982	−	0.996851i	$-0.474732\pi$
$647$	4.03409	0.158596	0.0792982	+	0.996851i	$0.474732\pi$
$648$	78.7627	3.09409
$649$	35.4403	1.39115
$650$	3.85068	0.151036
$651$	−65.3025	−2.55941
$652$	53.2635	2.08596
$653$	−10.3611	−0.405462	−0.202731	−	0.979234i	$-0.564982\pi$
$653$	−10.3611	−0.405462	−0.202731	+	0.979234i	$0.564982\pi$
$654$	−44.8601	−1.75417
$655$	−1.01208	−0.0395451
$656$	120.434	4.70217
$657$	−0.0557932	−0.00217670
$658$	−32.0481	−1.24937
$659$	40.9525	1.59528	0.797642	−	0.603132i	$-0.206081\pi$
$659$	40.9525	1.59528	0.797642	+	0.603132i	$0.206081\pi$
$660$	81.0954	3.15664
$661$	−3.10065	−0.120601	−0.0603006	−	0.998180i	$-0.519206\pi$
$661$	−3.10065	−0.120601	−0.0603006	+	0.998180i	$0.519206\pi$
$662$	−79.0458	−3.07220
$663$	5.69233	0.221072
$664$	129.354	5.01991
$665$	19.9352	0.773053
$666$	−0.142264	−0.00551260
$667$	−16.8716	−0.653272
$668$	77.1833	2.98631
$669$	−42.7858	−1.65419
$670$	69.4187	2.68188
$671$	35.8370	1.38347
$672$	126.586	4.88315
$673$	−2.58314	−0.0995727	−0.0497864	−	0.998760i	$-0.515854\pi$
$673$	−2.58314	−0.0995727	−0.0497864	+	0.998760i	$0.515854\pi$
$674$	25.6582	0.988318
$675$	−7.42372	−0.285739
$676$	5.24211	0.201620
$677$	−26.5848	−1.02174	−0.510868	−	0.859659i	$-0.670676\pi$
$677$	−26.5848	−1.02174	−0.510868	+	0.859659i	$0.670676\pi$
$678$	−72.0002	−2.76515
$679$	1.58611	0.0608691
$680$	72.6047	2.78426
$681$	5.64811	0.216436
$682$	−85.5483	−3.27582
$683$	2.60182	0.0995560	0.0497780	−	0.998760i	$-0.484149\pi$
$683$	2.60182	0.0995560	0.0497780	+	0.998760i	$0.484149\pi$
$684$	−0.0904361	−0.00345791
$685$	49.8551	1.90487
$686$	37.4666	1.43048
$687$	−26.2004	−0.999606
$688$	98.9674	3.77310
$689$	8.73856	0.332913
$690$	−31.6781	−1.20597
$691$	12.2145	0.464660	0.232330	−	0.972637i	$-0.425365\pi$
$691$	12.2145	0.464660	0.232330	+	0.972637i	$0.425365\pi$
$692$	−50.4488	−1.91778
$693$	−0.133848	−0.00508445
$694$	−26.4729	−1.00490
$695$	−41.7577	−1.58396
$696$	95.4265	3.61713
$697$	−30.4106	−1.15188
$698$	65.5628	2.48159
$699$	23.0222	0.870778
$700$	−31.2374	−1.18066
$701$	34.6697	1.30946	0.654728	−	0.755865i	$-0.272783\pi$
$701$	34.6697	1.30946	0.654728	+	0.755865i	$0.272783\pi$
$702$	−13.9621	−0.526965
$703$	−10.9186	−0.411804
$704$	74.4290	2.80515
$705$	−12.5795	−0.473771
$706$	−97.2784	−3.66112
$707$	35.4104	1.33174
$708$	91.6414	3.44410
$709$	−29.6891	−1.11500	−0.557499	−	0.830177i	$-0.688239\pi$
$709$	−29.6891	−1.11500	−0.557499	+	0.830177i	$0.688239\pi$
$710$	−31.2371	−1.17231
$711$	−0.0342885	−0.00128592
$712$	−70.6861	−2.64907
$713$	24.1889	0.905881
$714$	−63.7949	−2.38746
$715$	−8.91803	−0.333515
$716$	−30.8046	−1.15122
$717$	11.0880	0.414089
$718$	−35.2082	−1.31396
$719$	−0.0816762	−0.00304601	−0.00152301	−	0.999999i	$-0.500485\pi$
$719$	−0.0816762	−0.00304601	−0.00152301	+	0.999999i	$0.500485\pi$
$720$	0.301192	0.0112248
$721$	−53.5373	−1.99384
$722$	41.5422	1.54604
$723$	−25.0356	−0.931084
$724$	70.0328	2.60275
$725$	−9.02176	−0.335060
$726$	−6.38183	−0.236852
$727$	−36.2335	−1.34383	−0.671913	−	0.740630i	$-0.734527\pi$
$727$	−36.2335	−1.34383	−0.671913	+	0.740630i	$0.734527\pi$
$728$	−36.3349	−1.34666
$729$	26.9172	0.996935
$730$	41.6615	1.54196
$731$	−24.9900	−0.924290
$732$	92.6672	3.42508
$733$	43.9886	1.62476	0.812378	−	0.583132i	$-0.198173\pi$
$733$	43.9886	1.62476	0.812378	+	0.583132i	$0.198173\pi$
$734$	−34.1005	−1.25867
$735$	45.4995	1.67828
$736$	−46.8890	−1.72835
$737$	−35.7719	−1.31767
$738$	−0.227931	−0.00839024
$739$	25.5493	0.939845	0.469922	−	0.882708i	$-0.344282\pi$
$739$	25.5493	0.939845	0.469922	+	0.882708i	$0.344282\pi$
$740$	76.8933	2.82666
$741$	3.27448	0.120291
$742$	−97.9345	−3.59529
$743$	−47.6410	−1.74778	−0.873889	−	0.486125i	$-0.838410\pi$
$743$	−47.6410	−1.74778	−0.873889	+	0.486125i	$0.838410\pi$
$744$	−136.813	−5.01581
$745$	29.3080	1.07376
$746$	21.1830	0.775565
$747$	−0.135498	−0.00495762
$748$	−60.4935	−2.21186
$749$	−26.8885	−0.982483
$750$	42.2522	1.54283
$751$	5.46057	0.199259	0.0996296	−	0.995025i	$-0.468234\pi$
$751$	5.46057	0.199259	0.0996296	+	0.995025i	$0.468234\pi$
$752$	−37.1621	−1.35516
$753$	47.5830	1.73402
$754$	−16.9676	−0.617922
$755$	17.9007	0.651473
$756$	113.263	4.11933
$757$	7.26320	0.263986	0.131993	−	0.991251i	$-0.457862\pi$
$757$	7.26320	0.263986	0.131993	+	0.991251i	$0.457862\pi$
$758$	−0.880240	−0.0319717
$759$	16.3239	0.592521
$760$	41.7655	1.51499
$761$	2.62445	0.0951361	0.0475680	−	0.998868i	$-0.484853\pi$
$761$	2.62445	0.0951361	0.0475680	+	0.998868i	$0.484853\pi$
$762$	22.1307	0.801711
$763$	−40.0193	−1.44880
$764$	59.9888	2.17032
$765$	−0.0760533	−0.00274971
$766$	−5.66750	−0.204775
$767$	−10.0778	−0.363887
$768$	28.8578	1.04132
$769$	−12.4904	−0.450416	−0.225208	−	0.974311i	$-0.572306\pi$
$769$	−12.4904	−0.450416	−0.225208	+	0.974311i	$0.572306\pi$
$770$	99.9458	3.60180
$771$	−23.1231	−0.832758
$772$	99.9471	3.59718
$773$	−4.38713	−0.157794	−0.0788971	−	0.996883i	$-0.525140\pi$
$773$	−4.38713	−0.157794	−0.0788971	+	0.996883i	$0.525140\pi$
$774$	−0.187303	−0.00673247
$775$	12.9345	0.464621
$776$	3.32300	0.119289
$777$	−41.7861	−1.49907
$778$	−53.0358	−1.90143
$779$	−17.4935	−0.626771
$780$	−23.0602	−0.825687
$781$	16.0967	0.575984
$782$	23.6304	0.845023
$783$	32.7118	1.16902
$784$	134.414	4.80050
$785$	−24.0022	−0.856676
$786$	1.86308	0.0664539
$787$	−37.1943	−1.32583	−0.662917	−	0.748693i	$-0.730682\pi$
$787$	−37.1943	−1.32583	−0.662917	+	0.748693i	$0.730682\pi$
$788$	90.7237	3.23190
$789$	32.7123	1.16459
$790$	25.6037	0.910938
$791$	−64.2308	−2.28378
$792$	−0.280420	−0.00996428
$793$	−10.1906	−0.361878
$794$	24.3552	0.864335
$795$	−38.4412	−1.36337
$796$	−38.6172	−1.36875
$797$	−18.2235	−0.645508	−0.322754	−	0.946483i	$-0.604609\pi$
$797$	−18.2235	−0.645508	−0.322754	+	0.946483i	$0.604609\pi$
$798$	−36.6977	−1.29908
$799$	9.38372	0.331972
$800$	−25.0729	−0.886462
$801$	0.0740435	0.00261620
$802$	70.9203	2.50428
$803$	−21.4684	−0.757605
$804$	−92.4988	−3.26218
$805$	−28.2598	−0.996027
$806$	24.3264	0.856862
$807$	−15.3829	−0.541504
$808$	74.1871	2.60989
$809$	42.3095	1.48752	0.743761	−	0.668445i	$-0.233040\pi$
$809$	42.3095	1.48752	0.743761	+	0.668445i	$0.233040\pi$
$810$	61.6066	2.16464
$811$	40.1520	1.40993	0.704964	−	0.709243i	$-0.250963\pi$
$811$	40.1520	1.40993	0.704964	+	0.709243i	$0.250963\pi$
$812$	137.644	4.83035
$813$	52.0782	1.82646
$814$	−54.7410	−1.91867
$815$	25.7667	0.902567
$816$	−73.9748	−2.58964
$817$	−14.3754	−0.502931
$818$	53.4325	1.86822
$819$	0.0380607	0.00132995
$820$	123.196	4.30220
$821$	19.1213	0.667338	0.333669	−	0.942690i	$-0.391713\pi$
$821$	19.1213	0.667338	0.333669	+	0.942690i	$0.391713\pi$
$822$	−91.7759	−3.20105
$823$	−21.0242	−0.732858	−0.366429	−	0.930446i	$-0.619420\pi$
$823$	−21.0242	−0.732858	−0.366429	+	0.930446i	$0.619420\pi$
$824$	−112.164	−3.90743
$825$	8.72889	0.303901
$826$	112.943	3.92980
$827$	−30.7354	−1.06878	−0.534388	−	0.845239i	$-0.679458\pi$
$827$	−30.7354	−1.06878	−0.534388	+	0.845239i	$0.679458\pi$
$828$	0.128201	0.00445529
$829$	25.2701	0.877666	0.438833	−	0.898569i	$-0.355392\pi$
$829$	25.2701	0.877666	0.438833	+	0.898569i	$0.355392\pi$
$830$	101.178	3.51195
$831$	40.4542	1.40334
$832$	−21.1645	−0.733749
$833$	−33.9406	−1.17597
$834$	76.8697	2.66178
$835$	37.3381	1.29214
$836$	−34.7986	−1.20353
$837$	−46.8989	−1.62106
$838$	−5.48369	−0.189431
$839$	−20.0713	−0.692938	−0.346469	−	0.938061i	$-0.612619\pi$
$839$	−20.0713	−0.692938	−0.346469	+	0.938061i	$0.612619\pi$
$840$	159.838	5.51494
$841$	10.7533	0.370805
$842$	−103.524	−3.56768
$843$	47.6221	1.64019
$844$	70.9523	2.44228
$845$	2.53592	0.0872383
$846$	0.0703320	0.00241806
$847$	−5.69317	−0.195620
$848$	−113.562	−3.89974
$849$	3.02051	0.103664
$850$	12.6359	0.433407
$851$	15.4781	0.530582
$852$	41.6227	1.42597
$853$	36.7702	1.25899	0.629493	−	0.777006i	$-0.283262\pi$
$853$	36.7702	1.25899	0.629493	+	0.777006i	$0.283262\pi$
$854$	114.207	3.90810
$855$	−0.0437493	−0.00149619
$856$	−56.3331	−1.92543
$857$	38.4669	1.31400	0.657002	−	0.753889i	$-0.271824\pi$
$857$	38.4669	1.31400	0.657002	+	0.753889i	$0.271824\pi$
$858$	16.4168	0.560459
$859$	−27.9594	−0.953962	−0.476981	−	0.878913i	$-0.658269\pi$
$859$	−27.9594	−0.953962	−0.476981	+	0.878913i	$0.658269\pi$
$860$	101.237	3.45216
$861$	−66.9484	−2.28160
$862$	97.6801	3.32700
$863$	−26.2017	−0.891915	−0.445958	−	0.895054i	$-0.647137\pi$
$863$	−26.2017	−0.891915	−0.445958	+	0.895054i	$0.647137\pi$
$864$	90.9113	3.09287
$865$	−24.4051	−0.829797
$866$	92.7452	3.15161
$867$	−10.8105	−0.367143
$868$	−197.340	−6.69816
$869$	−13.1937	−0.447567
$870$	74.6408	2.53056
$871$	10.1721	0.344667
$872$	−83.8432	−2.83929
$873$	−0.00348083	−0.000117808 0
$874$	13.5933	0.459800
$875$	37.6929	1.27425
$876$	−55.5130	−1.87561
$877$	−33.2638	−1.12324	−0.561620	−	0.827395i	$-0.689822\pi$
$877$	−33.2638	−1.12324	−0.561620	+	0.827395i	$0.689822\pi$
$878$	−99.5052	−3.35814
$879$	36.0300	1.21526
$880$	115.895	3.90680
$881$	−9.81798	−0.330776	−0.165388	−	0.986229i	$-0.552888\pi$
$881$	−9.81798	−0.330776	−0.165388	+	0.986229i	$0.552888\pi$
$882$	−0.254388	−0.00856570
$883$	−3.17594	−0.106879	−0.0534395	−	0.998571i	$-0.517018\pi$
$883$	−3.17594	−0.106879	−0.0534395	+	0.998571i	$0.517018\pi$
$884$	17.2018	0.578561
$885$	44.3323	1.49022
$886$	−20.1962	−0.678506
$887$	−17.2616	−0.579589	−0.289795	−	0.957089i	$-0.593587\pi$
$887$	−17.2616	−0.579589	−0.289795	+	0.957089i	$0.593587\pi$
$888$	−87.5445	−2.93780
$889$	19.7426	0.662146
$890$	−55.2893	−1.85330
$891$	−31.7463	−1.06354
$892$	−129.296	−4.32915
$893$	5.39794	0.180635
$894$	−53.9516	−1.80441
$895$	−14.9020	−0.498119
$896$	91.2481	3.04838
$897$	−4.64185	−0.154987
$898$	−25.6680	−0.856553
$899$	−56.9944	−1.90087
$900$	0.0685528	0.00228509
$901$	28.6753	0.955314
$902$	−87.7046	−2.92024
$903$	−55.0152	−1.83079
$904$	−134.568	−4.47566
$905$	33.8790	1.12618
$906$	−32.9525	−1.09477
$907$	22.2744	0.739609	0.369804	−	0.929110i	$-0.379425\pi$
$907$	22.2744	0.739609	0.369804	+	0.929110i	$0.379425\pi$
$908$	17.0682	0.566429
$909$	−0.0777108	−0.00257750
$910$	−28.4205	−0.942130
$911$	−5.02702	−0.166552	−0.0832762	−	0.996527i	$-0.526538\pi$
$911$	−5.02702	−0.166552	−0.0832762	+	0.996527i	$0.526538\pi$
$912$	−42.5536	−1.40909
$913$	−52.1378	−1.72551
$914$	13.8823	0.459185
$915$	44.8286	1.48199
$916$	−79.1758	−2.61604
$917$	1.66204	0.0548853
$918$	−45.8162	−1.51216
$919$	−12.6591	−0.417586	−0.208793	−	0.977960i	$-0.566953\pi$
$919$	−12.6591	−0.417586	−0.208793	+	0.977960i	$0.566953\pi$
$920$	−59.2061	−1.95197
$921$	26.3812	0.869289
$922$	−36.7640	−1.21076
$923$	−4.57723	−0.150661
$924$	−133.176	−4.38115
$925$	8.27659	0.272133
$926$	−2.69112	−0.0884356
$927$	0.117492	0.00385894
$928$	110.481	3.62672
$929$	4.31472	0.141561	0.0707807	−	0.997492i	$-0.477451\pi$
$929$	4.31472	0.141561	0.0707807	+	0.997492i	$0.477451\pi$
$930$	−107.013	−3.50908
$931$	−19.5241	−0.639878
$932$	69.5715	2.27889
$933$	−40.6957	−1.33232
$934$	−70.2599	−2.29897
$935$	−29.2643	−0.957043
$936$	0.0797398	0.00260638
$937$	−22.2556	−0.727060	−0.363530	−	0.931583i	$-0.618429\pi$
$937$	−22.2556	−0.727060	−0.363530	+	0.931583i	$0.618429\pi$
$938$	−114.000	−3.72223
$939$	−9.90408	−0.323208
$940$	−38.0144	−1.23989
$941$	54.4403	1.77470	0.887351	−	0.461095i	$-0.152543\pi$
$941$	54.4403	1.77470	0.887351	+	0.461095i	$0.152543\pi$
$942$	44.1845	1.43961
$943$	24.7986	0.807552
$944$	130.966	4.26258
$945$	54.7918	1.78238
$946$	−72.0716	−2.34325
$947$	12.9348	0.420323	0.210162	−	0.977667i	$-0.432601\pi$
$947$	12.9348	0.420323	0.210162	+	0.977667i	$0.432601\pi$
$948$	−34.1163	−1.10805
$949$	6.10474	0.198168
$950$	7.26873	0.235829
$951$	9.95469	0.322803
$952$	−119.232	−3.86433
$953$	38.6919	1.25336	0.626678	−	0.779279i	$-0.284414\pi$
$953$	38.6919	1.25336	0.626678	+	0.779279i	$0.284414\pi$
$954$	0.214925	0.00695845
$955$	29.0201	0.939068
$956$	33.5073	1.08370
$957$	−38.4628	−1.24333
$958$	46.5914	1.50530
$959$	−81.8725	−2.64380
$960$	93.1034	3.00490
$961$	50.7130	1.63590
$962$	15.5661	0.501871
$963$	0.0590088	0.00190153
$964$	−75.6560	−2.43672
$965$	48.3503	1.55645
$966$	52.0221	1.67378
$967$	−50.0150	−1.60838	−0.804188	−	0.594375i	$-0.797399\pi$
$967$	−50.0150	−1.60838	−0.804188	+	0.594375i	$0.797399\pi$
$968$	−11.9276	−0.383367
$969$	10.7451	0.345183
$970$	2.59918	0.0834547
$971$	7.29332	0.234054	0.117027	−	0.993129i	$-0.462664\pi$
$971$	7.29332	0.234054	0.117027	+	0.993129i	$0.462664\pi$
$972$	−0.497887	−0.0159697
$973$	68.5748	2.19841
$974$	−51.8616	−1.66175
$975$	−2.48214	−0.0794920
$976$	132.432	4.23904
$977$	−3.76475	−0.120445	−0.0602225	−	0.998185i	$-0.519181\pi$
$977$	−3.76475	−0.120445	−0.0602225	+	0.998185i	$0.519181\pi$
$978$	−47.4326	−1.51673
$979$	28.4909	0.910573
$980$	137.497	4.39217
$981$	0.0878255	0.00280405
$982$	57.2688	1.82752
$983$	−17.9385	−0.572149	−0.286075	−	0.958207i	$-0.592351\pi$
$983$	−17.9385	−0.572149	−0.286075	+	0.958207i	$0.592351\pi$
$984$	−140.261	−4.47137
$985$	43.8884	1.39840
$986$	−55.6786	−1.77317
$987$	20.6581	0.657555
$988$	9.89528	0.314811
$989$	20.3783	0.647993
$990$	−0.219339	−0.00697104
$991$	15.4438	0.490589	0.245295	−	0.969449i	$-0.421115\pi$
$991$	15.4438	0.490589	0.245295	+	0.969449i	$0.421115\pi$
$992$	−158.397	−5.02910
$993$	50.9527	1.61694
$994$	51.2978	1.62707
$995$	−18.6814	−0.592241
$996$	−134.818	−4.27186
$997$	−16.6367	−0.526889	−0.263444	−	0.964675i	$-0.584859\pi$
$997$	−16.6367	−0.526889	−0.263444	+	0.964675i	$0.584859\pi$
$998$	106.162	3.36049
$999$	−30.0099	−0.949471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.4	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.4	✓	123	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69112 q^{2} +1.73469 q^{3} +5.24211 q^{4} +2.53592 q^{5} -4.66825 q^{6} -4.16450 q^{7} -8.72491 q^{8} +0.00913932 q^{9} +O(q^{10})\)	\(q-2.69112 q^{2} +1.73469 q^{3} +5.24211 q^{4} +2.53592 q^{5} -4.66825 q^{6} -4.16450 q^{7} -8.72491 q^{8} +0.00913932 q^{9} -6.82446 q^{10} +3.51668 q^{11} +9.09343 q^{12} -1.00000 q^{13} +11.2072 q^{14} +4.39903 q^{15} +12.9955 q^{16} -3.28147 q^{17} -0.0245950 q^{18} -1.88765 q^{19} +13.2936 q^{20} -7.22411 q^{21} -9.46381 q^{22} +2.67590 q^{23} -15.1350 q^{24} +1.43088 q^{25} +2.69112 q^{26} -5.18821 q^{27} -21.8308 q^{28} -6.30503 q^{29} -11.8383 q^{30} +9.03952 q^{31} -17.5227 q^{32} +6.10035 q^{33} +8.83083 q^{34} -10.5608 q^{35} +0.0479094 q^{36} +5.78425 q^{37} +5.07989 q^{38} -1.73469 q^{39} -22.1257 q^{40} +9.26736 q^{41} +19.4409 q^{42} +7.61549 q^{43} +18.4349 q^{44} +0.0231766 q^{45} -7.20117 q^{46} -2.85961 q^{47} +22.5432 q^{48} +10.3431 q^{49} -3.85068 q^{50} -5.69233 q^{51} -5.24211 q^{52} -8.73856 q^{53} +13.9621 q^{54} +8.91803 q^{55} +36.3349 q^{56} -3.27448 q^{57} +16.9676 q^{58} +10.0778 q^{59} +23.0602 q^{60} +10.1906 q^{61} -24.3264 q^{62} -0.0380607 q^{63} +21.1645 q^{64} -2.53592 q^{65} -16.4168 q^{66} -10.1721 q^{67} -17.2018 q^{68} +4.64185 q^{69} +28.4205 q^{70} +4.57723 q^{71} -0.0797398 q^{72} -6.10474 q^{73} -15.5661 q^{74} +2.48214 q^{75} -9.89528 q^{76} -14.6452 q^{77} +4.66825 q^{78} -3.75175 q^{79} +32.9556 q^{80} -9.02733 q^{81} -24.9396 q^{82} -14.8258 q^{83} -37.8696 q^{84} -8.32155 q^{85} -20.4942 q^{86} -10.9372 q^{87} -30.6828 q^{88} +8.10164 q^{89} -0.0623709 q^{90} +4.16450 q^{91} +14.0274 q^{92} +15.6807 q^{93} +7.69554 q^{94} -4.78693 q^{95} -30.3964 q^{96} -0.380863 q^{97} -27.8345 q^{98} +0.0321401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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